Kevin Brown was discussing only Schwarzschild solution to the EFE. The geometry where there's a coordinate singularity at r=2M. Very useful for modeling the weak field and for predicting the remote bkkpr observations like 'dying pulse trains'. Where did I say this? "The notion that space is falling inward in a gravitational field is "crank". If it comforts you to defend that idea by calling me names, that's up to you, but be warned that people will see right through it.' I never said anything about 'space is falling inward in a gravitational field'. You just think so because you don't understand the rain metric and think it must be like 'something you heard in the past'. You don't understand there's more than one solution to the EFE so you can't know much about GR. You think the rain metric predicts space is being sucked into the black hole. It doesn't. The difference between the rain metric and the Schwarzschild metric is the measurements are being made from different frames of reference. A remote bookkeeper frame with a coordinate singularity at r=2M and a local proper frame with no coordinate singularity along it's entire radial path to r=0. You are a crank putting 'putting dumb words in my mouth' based on your inability to understand the difference between these two metric solutions to the EFE. BTW black holes rotate. Read Project F that I linked. That's not the first time you've put 'words in my mouth' based on YOUR ignorance of the subject under discussion. Everybody who understands this science knows your full of crap. You probably haven't noticed since your observational skills are somewhat messed up.
You said that better than me. Your query 'in the last sentence' is probably beyond his ability to comprehend.
Trivially. See stress-energy tensor on wikipedia along with this. The EFEs deal with energy density, flux, pressure, and shear stress. There are no terms for space falling down. I'm not cherry-picking, I'm giving a relevant passage. Bruce and I have referred to Kevin Brown before. And yes, I can refute the argument given in the paper in favour of the point-singularity. Start a thread and ask a question or state a position and I'll give my reply. Because they're non-real solutions. In GR we say that all coordinate systems are equally valid, but this does not extend to coordinate systems that do not exist. No, I've explained an issue with the Kerr metric, which you have not addressed. I can show you the fatal problem with that proper time. Best start a new thread.
You're strong willed, decisive and quick to form opinions. Given the right circumstances, you could make a good leader, and influence others. However, that may actually not be well suited for science forums, especially theoretical physics. It's less to do with one's level of education, and more about personality type. Just my analysis. Back to the topic. You claim I lack the math knowledge, so let me explain. I've considered a single point mass moving in a 2-D plane. The displacement of the object w.r.t. time is described by two parametric equations. By applying the sine rule, we can formulate an equation for the magnitude of the specific angular momentum and torque. The radius is defined from the origin in the y-displacement-x-displacement graph, which is otherwise known as our 2-D plane. When the acceleration vector is pointing towards or away from the origin, based on the equations we can see that torque is zero. And hence angular momentum is constant. You can try it for yourself. I've put modulus signs because I haven't examined if the positive or negative magnitudes also correspond to clockwise and counter-clockwise directions.
Yes. Other coordinate systems treat that as a mere artefact of no physical signifance. Big mistake. I understand it, see this, and stop being abusive just because you can't address that issue with the Kerr metric.
Oh, now I think I know what you're asking. The proof in this section is broken into the three parts for easier digestion. Does this help? http://www.lightandmatter.com/html_books/lm/ch15/ch15.html#Section15.7
Dude, that comment made me throw up in my mouth a little bit. Tach is proficient at math but hypercritical of everyone and is incapable of admitting errors himself. He lacks maturity and I would imagine that most people would agree with that assessment.
Cranks link stuff they don't understand to pretend they do. Everything you say reveals how little you know about the subject matter. It's a coordinate singularity not physical. The Kerr metric has a coordinate singularity somewhere between r_H < 2M and r=M. How about you tell me where it is if a=.8? The link is a Project in the 1st edition of Exploring Black Holes so that must be a draft from the 2nd edition which is going to be released November 1st. I should get my pre-ordered copy shortly thereafter. This is a very interesting derivation from that project. Forgot to say 'in geometric units' Derive dr/dTau [measured in the proper frame of the 'Rain drop']. E/m = (1-2M/r)dt/dTau = 1 [Energy per unit mass constant of the motion] Rewrite dTau = (1-2M/r) dt_bkkpr dr/dt_bkkpr = -(1-2M/r)(2M/r)^1/2 [this predicts dr/dt_bkkpr=0 at r=2M] Rewrite dr = -(1-2M/r)(2M/r)^1/2 dt_bkkpr Solve for dr/dTau dr/dTau = -(1-2M/r)(2M/r)^1/2 dt_bkkpr / (1-2M/r) dt_bkkpr = -(2M/r)^1/2 [ticks are measured in the proper frame of the falling Raindrop]. Integrate dt_rain = -(dr/(2M/r)^1/2 = -(r^1/2 dr/(2M)^1/2 = - int (r^1/2 dr/(2M)^1/2 = 1/(2M/r)^1/2 int r^1/2 dr dt_rain = 1/3(2/M)^1/2 r^3/2 Build the model t_2 rain - t_1rain = 1/3(2/M)^1/2 (r^3/2_1 - r^3/2_2) This 'fun' derivation can be used to predict the proper time it takes for the Raindrop observer to fall from r1 to r2. All the way to r=0 if you want since the Rain metric doesn't have a coordinate singularity at r=2M. When you set r2=0 you don't need the model just dt_rain = 1/3(2/M)^1/2 r^3/2. Pretty cool.
The dumb stuff you say "Yes. Other coordinate systems treat that as a mere artefact of no physical signifance. Big mistake." That's the same as shouting at the top of your lungs: Look over here I don't understand this metric stuff at all. How about this whopper "I can show you the fatal problem with that proper time." How can you be this clueless and actually know what you're talking about? I conclude you don't and everything you've said about your ability is a crackpot fantasy. How about this "There are no terms for space falling down." You assumed this is what the rain metric predicted. Guess what it doesn't predict what you think it does. You brought up this bullshit. That's the same as shouting at the top of your lungs: Look over here I don't understand this metric stuff at all. There is a silver lining. The PHD's have received a short respite from having to correct all of your errors of admission and omission. Another good thing is you'll fit nicely on my growing ignore list.
Tach, Obviously you either missed post #95 or you ignored it. If you want to progress, you need to own your errors and address objections that are put to your ideas.
Don't fret. Please Register or Log in to view the hidden image! I still wrote a 2nd part. I mentioned "Given the right circumstances". So on a science forum, it works differently. Everyone has their strengths and weaknesses. Tach isn't nity-picky critical, but he is indeed very full of himself. And I disagree on the "proficient at math" part. When it comes to that, no one can compare to rpenner. Tach has probably insulted me the most, but I bear no ill feelings, cos its just a forum. Though if I were forced to deal with him IRL...*cocks gun*
Good stuff Trooper. Eram: I recommend you buy a paper copy of a book like this and sit down somewhere quiet and comfortable, and read it. Benjamin Crowell explains things well, and in an afternoon or two you can really improve your understanding. It can be much more productive than spending time on the internet asking lots and lots of questions. That's not to suggest you shouldn't spend time on the internet though. It's just a question of balance, and taking it up a level more quickly. brucep: stop being abusive, if you want me to explain it start a new thread. Meanwhile stay on topic.
Is that the same bcrowell on PF? I agree, forums aren't the most suitable learning environments. I think you and brucep should use the PM system.
Yes, you can view bcrowell's profile and see that his home page is http://www.lightandmatter.com/. Forums can be really good, but sitting down reading a book can be really good too. Sorry about bruce and the abuse. I'll try not to derail your thread.
Sometimes the dusty shelves of a library contain gems, all those "boring" books on physics and calculus. The internet on the other hand, is full of crap. Don't worry about it. You won't be able to outdo Martillo anyway.
